Machine Learning-Based Analysis and Anomaly Detection System for Factory Facility Operation Data

By adopting multi-module processing and feature extraction strategies in the abnormality detection system, the problem of difficulty in flexibly adjusting the feature extraction strategy in the prior art is solved, and efficient and accurate abnormality detection is achieved in complex equipment environments.

CN119720054BActive Publication Date: 2025-05-27CHAOWANG IND (CHENGDU) CO LTD
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Patent Information

Application Number
CN202510227802.4
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2025-02-28
Publication Date
2025-05-27
Estimated Expiration
2045-02-28

AI Technical Summary

Technical Problem

The prior art is difficult to flexibly adjust feature extraction strategies in abnormal detection, resulting in the inability to fully capture key abnormal patterns under specific needs, affecting the accuracy and adaptability of detection.

Method used

Through the machine learning-based factory equipment running data analysis and anomaly detection system, multi-module processing and feature extraction strategies are adopted, including feature extraction of time domain, frequency domain and wavelet transformation, data segmentation of sliding window and adaptive segmentation, feature selection of information gain method and principal component analysis, and construction of anomaly detection and evaluation model of BP neural network.

Benefits of technology

It realizes real-time and accurate detection of potential faults in complex equipment environments, improves the accuracy and adaptability of abnormal detection, and can flexibly adjust feature extraction strategies to adapt to the needs of different scenarios.

✦ Generated by Eureka AI based on patent content.

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Patent Text Reader

Abstract

The present invention discloses a plant equipment operation data analysis and anomaly detection system based on machine learning, which relates to the technical field of anomaly detection. It includes a first feature acquisition module for acquiring a first set of anomaly detection features; a second feature acquisition module for a second set of anomaly detection features; merging the first set of anomaly detection features and the second set of anomaly detection features to construct several different sets of anomaly detection features to be screened; an anomaly detection evaluation module for obtaining the model generalization data and detection effect data of anomaly detection, and constructing an anomaly detection evaluation model based on a BP neural network; constructing a feature set - anomaly detection effect display model, and performing curve analysis to obtain the screened anomaly detection features applied to the current anomaly detection, solving the problem that when performing anomaly detection in different scenarios, it is often difficult to flexibly adjust the feature extraction strategy, resulting in the inability to fully capture key anomaly patterns under specific requirements, affecting the accuracy and adaptability of detection.
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Description

Technical Field

[0001] The present invention relates to the field of anomaly detection technology, and more specifically, to a factory equipment operation data analysis and anomaly detection system based on machine learning. Background Art

[0002] Factory equipment operation data analysis and anomaly detection is a monitoring and evaluation technology based on equipment operation data, which aims to identify whether the equipment has abnormalities, warn of potential faults in advance, and ensure production safety and equipment stability. Its core processes include data acquisition, feature extraction, anomaly detection and fault diagnosis. In the data acquisition stage, sensors are used to collect various operating parameters of the equipment, such as temperature, pressure, vibration, etc., while feature extraction converts these raw data into analyzable features so that the model can identify potential abnormal patterns. Feature extraction methods include time domain features (such as mean, variance, kurtosis, etc.), frequency domain features (such as power spectral density, spectrum features) and time-frequency domain features (such as wavelet transform, short-time Fourier transform), etc. These features can effectively reflect the operating status and change trends of the equipment.

[0003] Existing anomaly detection technologies mainly include statistical methods, machine learning methods, and deep learning methods. Statistical methods often detect anomalies by setting thresholds and identifying anomalies by comparing the differences between historical anomaly detection data and real-time data. Machine learning methods, such as support vector machines (SVM), decision trees, K-nearest neighbors (K-NN), etc., can establish anomaly detection models through training data and are more adaptable. Deep learning methods, such as autoencoders and convolutional neural networks (CNNs), can automatically learn features from large amounts of data and perform anomaly detection, and are suitable for complex and nonlinear anomaly patterns. These technologies are usually combined with feature selection and dimensionality reduction algorithms in applications to optimize detection results, reduce the risk of false positives and false negatives, and improve the accuracy and robustness of the system.

[0004] For example, the invention patent with announcement number: CN117851954B announces a bearing processing equipment operation quality detection system and method based on data analysis, including importing the bearing production data produced by the acquired processing equipment into the bearing production data abnormal value calculation strategy to calculate the bearing production data abnormal value of the bearing processing equipment, substituting the calculated equipment operation abnormal value and bearing production data abnormal value into the equipment fault judgment strategy to calculate the equipment fault value, and comparing the calculated equipment fault value with the set equipment fault threshold. If the equipment fault value is greater than or equal to the set equipment fault threshold, the part with the highest probability of equipment failure is output to remind maintenance personnel to perform equipment maintenance. If the equipment fault value is less than the set equipment fault threshold, no maintenance is required, and the equipment fault and fault location are accurately judged and identified through the equipment operation data and bearing production data.

[0005] For example, the invention patent with announcement number: CN113190421B discloses a method for detecting and analyzing the health status of equipment in a data center, including: collecting real-time operation data of the equipment in the data center, and transmitting the real-time operation data to the data analysis terminal; the data analysis terminal analyzes the real-time operation data, and determines whether the health status of the equipment in the data center is abnormal; if the health status of the equipment in the data center is abnormal, the judgment result is transmitted to the operation and maintenance terminal to find the cause of the abnormal failure of the equipment in the data center; if the health status of the equipment in the data center is normal, the development trend of the health status of the equipment in the data center is predicted according to the analysis result, and factors related to potential failures are found. By analyzing the real-time operation data of the equipment in the computer room, finding out the cause of the abnormal equipment according to the analysis result, and discovering and handling possible failures in advance, the efficiency of detecting the health status of the equipment is improved, and the purpose of preventing problems before they occur is achieved.

[0006] In the above-disclosed technical solution, there are at least the following technical problems: In anomaly detection, the dimension of the feature directly affects the performance of the model, especially when processing complex equipment operation data, how to choose the appropriate feature dimension is the key. High-dimensional features can more comprehensively reflect the operating status of the equipment by extracting rich information from a variety of sensors and data sources, but high-dimensional features also bring about the problem of "dimensionality disaster", resulting in a significant increase in computing costs and storage requirements, and may introduce redundant features, increasing the complexity of data processing. In addition, redundant or irrelevant features in high-dimensional data may interfere with the identification of abnormal signals and reduce the efficiency and accuracy of the detection model. On the contrary, low-dimensional features reduce the consumption of computing resources by simplifying the data dimension, but this simplification may lead to the loss of important detailed information and fail to fully capture the complex changes in equipment operation, thereby increasing the risk of underreporting, especially in multi-factor intertwined failure modes, low-dimensional features are often insufficient to accurately describe abnormal behavior;

[0007] When performing anomaly detection according to different scenarios, existing technologies often find it difficult to flexibly adjust feature extraction strategies, resulting in the inability to fully capture key abnormal patterns under specific needs, affecting the accuracy and adaptability of detection.

[0008] In view of the above problems, the present invention proposes a solution. Summary of the invention

[0009] In order to overcome the above-mentioned defects of the prior art, an embodiment of the present invention provides a factory equipment operation data analysis and anomaly detection system based on machine learning, which analyzes feature extraction of different dimensions to solve the problem that it is often difficult to flexibly adjust the feature extraction strategy when performing anomaly detection in different scenarios, resulting in the inability to fully capture key abnormal patterns under specific needs, affecting the accuracy and adaptability of detection.

[0010] To achieve the above object, the present invention provides the following technical solutions:

[0011] A factory equipment operation data analysis and anomaly detection system based on machine learning, comprising a first feature acquisition module, a second feature acquisition module, a feature selection module, an anomaly detection evaluation module, and an anomaly detection application module;

[0012] A first feature acquisition module is used to acquire factory equipment operation data, perform data transformation and feature extraction on the factory equipment operation data based on a first data transformation method set, and obtain a first anomaly detection feature set;

[0013] A second feature acquisition module is used to perform data segmentation of different window sizes on the factory equipment operation data based on a second data segmentation method and perform feature extraction to obtain a second anomaly detection feature set;

[0014] A feature selection module is used to merge the first anomaly detection feature set and the second anomaly detection feature set to obtain a third anomaly detection feature set, and perform several dimension-up and dimension-down feature selections based on information gain method and principal component analysis to construct several groups of different anomaly detection feature sets to be screened;

[0015] The anomaly detection evaluation module is used to perform anomaly detection according to several different sets of anomaly detection feature sets to be screened, obtain model generalization data and detection effect data of anomaly detection, and build an anomaly detection evaluation model based on the BP neural network;

[0016] The anomaly detection application module is used to build a feature set-anomaly detection effect display model based on each set of anomaly detection feature sets to be screened and the corresponding anomaly detection evaluation model, and perform curve analysis to obtain the screened anomaly detection feature set for application to the current anomaly detection.

[0017] In a preferred embodiment, the first data transformation method includes time domain feature extraction, frequency domain feature extraction and wavelet transformation;

[0018] The data transformation and feature extraction of the factory equipment operation data based on the first data transformation method set is specifically:

[0019] By statistically analyzing the time series of plant equipment operation data, the mean, standard deviation, variance, kurtosis, and skewness are extracted as the basic distribution characteristics reflecting the equipment operation status;

[0020] Using Fourier transform, the time domain data is converted into frequency domain data, and the power spectrum density, frequency peak and bandwidth are extracted as periodicity and vibration characteristics;

[0021] The signal is decomposed into local features of different frequency bands through wavelet transform, and wavelet packet decomposition coefficients and wavelet energy features are extracted as burst features suitable for processing non-stationary signals.

[0022] A first anomaly detection feature set is constructed according to basic distribution characteristics, periodicity and vibration characteristics, and burst characteristics.

[0023] In a preferred embodiment, the second data segmentation method includes a sliding window method and an adaptive segmentation method;

[0024] The method for performing data segmentation of different window sizes on the factory equipment operation data based on the second data segmentation method and performing feature extraction is specifically:

[0025] The sliding window method uses a fixed-length time window to slide over the equipment operation data at a certain step length, gradually extracting the window data features in each window;

[0026] Adaptive segmentation method dynamically adjusts the window size according to the changes in the operating status of the equipment. When the equipment status is stable, a larger window is used to capture more information. When the equipment status changes dramatically, a smaller window is used to capture the changes in detail and perform data analysis to obtain the characteristics of the changed data.

[0027] A second anomaly detection feature set is constructed according to the change data features and the window data features.

[0028] In a preferred embodiment, the feature selection based on information gain method and principal component analysis is performed several times of dimension increase and dimension reduction to construct several groups of different anomaly detection feature sets to be screened, specifically:

[0029] Get the exception to be detected;

[0030] Calculate the information gain between each feature and the anomaly to be detected, and evaluate the importance of each feature in distinguishing the device status;

[0031] Select features with higher information gain;

[0032] Through multiple iterations, the feature set is gradually optimized, and the third anomaly detection feature set is subjected to several dimensionality reductions to obtain several anomaly detection feature sets to be screened;

[0033] Perform principal component analysis on the third anomaly detection feature set, and find the principal components in the data by calculating the covariance matrix of the features;

[0034] According to the variance of the principal components, a preset number of principal components are selected to perform feature dimensionality reduction;

[0035] Through the linear combination of principal components, several anomaly detection feature sets to be screened are generated;

[0036] The third anomaly detection feature set is subjected to several dimensionality increase and dimensionality reduction operations to obtain several anomaly detection feature sets to be screened.

[0037] In a preferred embodiment, the model generalization data of the anomaly detection includes a model generalization coefficient of the anomaly detection model; the specific method for obtaining the model generalization coefficient is as follows:

[0038] Collect historical anomaly detection data of similar projects in the past. The historical anomaly detection data includes various types of anomaly detection features. Classify the collected anomaly detection feature records by type, assign feature weights to different types of features, and calculate the anomaly detection feature evaluation coefficient based on the type and weight of the problem record.

[0039] Obtain environmental factors that affect anomaly detection, including noise and transmission interference in the data collection environment, and calculate the impact of interference;

[0040] Obtain the type of plant equipment, the data type includes sensor data, and set a data score for the data type based on its impact on the accuracy of anomaly detection;

[0041] The model generalization coefficient is calculated by combining the interference effect, feature evaluation coefficient and data score.

[0042] In a preferred embodiment, the detection effect data includes a detection efficiency coefficient and an abnormality detection accuracy coefficient; the specific method for obtaining the detection efficiency coefficient is as follows:

[0043] Obtain the error margin between the model prediction value and the actual value of several sets of feature data in the anomaly detection process;

[0044] In the same time interval, the standard deviation and mean of the error margins were calculated;

[0045] Calculate the error amplitude variation coefficient based on the signal error amplitude standard deviation and mean value;

[0046] The error amplitude variation coefficient is used to calculate the detection efficiency coefficient based on a preset detection efficiency coefficient calculation formula.

[0047] In a preferred embodiment, the specific method for obtaining the anomaly detection accuracy coefficient is as follows:

[0048] Obtain the waveform of predicted values ​​and actual values ​​changing over time during anomaly detection;

[0049] Under the preset frequency, the harmonic composition of the predicted value signal and the actual value signal is obtained respectively, and the harmonic component analysis is performed to obtain the basic waveform component;

[0050] The basic waveform component is converted into the harmonic component by using the inverse Fourier transform; the floating value of the harmonic is calculated according to the ratio of the basic waveform component to the harmonic component;

[0051] Data analysis is performed on the harmonic floating values ​​to obtain the anomaly detection accuracy coefficient.

[0052] In a preferred embodiment, the feature set-anomaly detection effect display model is constructed according to each group of anomaly detection feature sets to be screened and the corresponding anomaly detection evaluation model, specifically:

[0053] Construct a vector set by combining the output of the anomaly detection evaluation model and the corresponding anomaly detection feature set to be screened;

[0054] Arrange the feature numbers of the to-be-screened anomaly detection feature sets of several vector sets from large to small as the X-axis, and the output of the corresponding anomaly detection evaluation model as the Y-axis to construct a rectangular coordinate system;

[0055] Several vector sets are marked on a rectangular coordinate system and smoothed using interpolation to construct a feature set-anomaly detection effect display model.

[0056] The technical effects and advantages of the factory equipment operation data analysis and anomaly detection system based on machine learning of the present invention are as follows:

[0057] 1. The present invention performs data processing and feature extraction through multiple modules. First, the first feature acquisition module performs data conversion such as time domain, frequency domain and wavelet transform on the equipment operation data to extract the operation characteristics of the equipment; secondly, the second feature acquisition module divides the data into different windows through the sliding window method and the adaptive segmentation method, and extracts the data features in the window. Then, the feature selection module optimizes the extracted features through the information gain method and principal component analysis, and selects the most representative feature set. Next, the anomaly detection evaluation module performs anomaly detection based on these feature sets, evaluates the generalization ability and detection effect of the model, and finally improves the accuracy and efficiency of anomaly detection. The combination of these steps helps to detect potential equipment failures in real time and accurately in complex equipment environments.

[0058] 2. The present invention can effectively evaluate the performance of different anomaly detection feature sets by constructing an anomaly detection evaluation model based on the BP neural network. By combining the model generalization coefficient, detection efficiency coefficient and anomaly detection accuracy coefficient, the model can not only improve the accuracy of anomaly detection, but also optimize the computational efficiency and generalization ability, thereby ensuring the adaptability and reliability of applications in various scenarios. By using the feature set and the anomaly detection effect display model for curve analysis, the most discriminative feature set can be systematically screened out. By analyzing the feature set, the features that can maximize the accuracy of anomaly detection and minimize the computational cost are selected, thereby improving the accuracy and efficiency of anomaly detection in practical applications. This method can flexibly adjust the feature extraction strategy during the anomaly detection process, solve the problem of not being able to fully capture key anomaly patterns in specific scenarios, and significantly improve the adaptability and accuracy of anomaly detection. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 It is a structural schematic diagram of the factory equipment operation data analysis and anomaly detection system based on machine learning of the present invention. DETAILED DESCRIPTION

[0060] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0061] Embodiment 1, Figure 1 The present invention provides a plant equipment operation data analysis and anomaly detection system based on machine learning, including a first feature acquisition module, a second feature acquisition module, a feature selection module, an anomaly detection evaluation module and an anomaly detection application module;

[0062] A first feature acquisition module is used to acquire factory equipment operation data, perform data transformation and feature extraction on the factory equipment operation data based on a first data transformation method set, and obtain a first anomaly detection feature set;

[0063] The first data transformation method includes time domain feature extraction, frequency domain feature extraction and wavelet transformation;

[0064] The data transformation and feature extraction of the factory equipment operation data based on the first data transformation method set is specifically:

[0065] By statistically analyzing the time series of plant equipment operation data, the mean, standard deviation, variance, kurtosis, and skewness are extracted as the basic distribution characteristics reflecting the equipment operation status;

[0066] Using Fourier transform, the time domain data is converted into frequency domain data, and the power spectrum density, frequency peak and bandwidth are extracted as periodicity and vibration characteristics;

[0067] The signal is decomposed into local features of different frequency bands through wavelet transform, and wavelet packet decomposition coefficients and wavelet energy features are extracted as burst features suitable for processing non-stationary signals.

[0068] A first anomaly detection feature set is constructed according to basic distribution characteristics, periodicity and vibration characteristics, and burst characteristics.

[0069] It should be noted that the main goal of the first data transformation method is to transform the original data to extract statistical information and patterns that reflect the characteristics of the data from different angles. These methods aim to extract features containing important information by converting the representation of data for subsequent analysis and modeling. This question only lists feasible methods, and the remaining original data transformations are still applicable.

[0070] It should be noted that in the time domain analysis process, it is necessary to ensure that the sampling frequency of the equipment operation data is high enough to capture the key characteristics of the equipment state changes. In particular, the calculation of statistics such as mean and standard deviation needs to be based on an appropriate time window to avoid losing details or over-smoothing.

[0071] Fourier transform and spectrum analysis need to focus on the periodic characteristics of time series signals, and frequency domain feature extraction may face certain challenges when processing non-periodic signals. Therefore, when selecting a spectrum analysis method, it is necessary to have a certain prior understanding of the frequency characteristics of the signal in order to more accurately identify periodic faults or anomalies.

[0072] Wavelet transform has advantages in processing non-stationary signals, but choosing the right wavelet basis and decomposition level is crucial. Too many decomposition levels may lead to redundant information, while too few levels may not be enough to capture fine-grained anomalies. Therefore, correctly setting the parameters of wavelet transform is the key to improving the accuracy of anomaly detection.

[0073] A second feature acquisition module is used to perform data segmentation of different window sizes on the factory equipment operation data based on a second data segmentation method and perform feature extraction to obtain a second anomaly detection feature set;

[0074] The second data segmentation method includes a sliding window method and an adaptive segmentation method;

[0075] The method for performing data segmentation of different window sizes on the factory equipment operation data based on the second data segmentation method and performing feature extraction is specifically:

[0076] The sliding window method uses a fixed-length time window to slide over the equipment operation data at a certain step length, gradually extracting the window data features in each window;

[0077] Adaptive segmentation method dynamically adjusts the window size according to the changes in the operating status of the equipment. When the equipment status is stable, a larger window is used to capture more information. When the equipment status changes dramatically, a smaller window is used to capture the changes in detail and perform data analysis to obtain the characteristics of the changed data.

[0078] A second anomaly detection feature set is constructed according to the change data features and the window data features.

[0079] It should be noted that in the sliding window method, within each window, statistics and spectral features such as mean, standard deviation, kurtosis, skewness, frequency domain features, etc. are calculated as candidate features for anomaly detection. The window length and step size can be adjusted according to the operating characteristics of the equipment and the characteristics of the abnormal pattern to optimize the effect of feature extraction;

[0080] The adaptive segmentation method can adjust the length of the window based on the degree of data change or other indicators (such as vibration amplitude, power spectrum density change, etc.), so as to adapt to different operating conditions of the equipment more flexibly.

[0081] The second data segmentation method (such as window size-based segmentation) focuses on dividing time series data into multiple subsequences, usually by defining time windows or sliding windows, and dividing the data according to different window sizes. Its purpose is to obtain features at different time scales through segmented data, thereby helping to identify time-varying patterns in device operation.

[0082] A feature selection module is used to merge the first anomaly detection feature set and the second anomaly detection feature set to obtain a third anomaly detection feature set, and perform several dimension-up and dimension-down feature selections based on information gain method and principal component analysis to construct several groups of different anomaly detection feature sets to be screened;

[0083] The feature selection based on information gain method and principal component analysis is performed several times of dimension increase and dimension reduction to construct several groups of different anomaly detection feature sets to be screened, specifically:

[0084] Get the exception to be detected;

[0085] The information gain between each feature and the anomaly to be detected is calculated to evaluate the importance of each feature in distinguishing the device status.

[0086] Select features with higher information gain and remove redundant features with lower information gain.

[0087] Through multiple iterations, the feature set is gradually optimized, and the third anomaly detection feature set is subjected to several dimensionality reductions to obtain several anomaly detection feature sets to be screened;

[0088] Perform principal component analysis on the third anomaly detection feature set and find the principal components in the data by calculating the covariance matrix of the features.

[0089] According to the variance of the principal components, a preset number of principal components are selected to perform feature dimensionality reduction;

[0090] Through the linear combination of principal components, several anomaly detection feature sets to be screened are generated;

[0091] The third anomaly detection feature set is subjected to several dimensionality increase and dimensionality reduction operations to obtain several anomaly detection feature sets to be screened.

[0092] It should be noted that the first anomaly detection feature set and the second anomaly detection feature set are combined to obtain a third anomaly detection feature set. These feature sets contain features extracted from multiple angles such as time domain, frequency domain, and wavelet transform, covering multi-dimensional information of device operation.

[0093] It should be noted that on the basis of the information gain method and PCA, several dimension increase and dimension reduction operations are performed. The dimension increase operation enhances the distinguishing ability of the feature space through feature construction (such as generating new features by combining existing features); the dimension reduction operation further eliminates redundant features, retains the most representative features, and reduces the complexity of the data; these multiple dimension increase and dimension reduction operations can help build a more refined and effective feature set, and improve the accuracy and efficiency of subsequent anomaly detection.

[0094] The anomaly detection evaluation module is used to perform anomaly detection according to several different sets of anomaly detection feature sets to be screened, obtain model generalization data and detection effect data of anomaly detection, and build an anomaly detection evaluation model based on the BP neural network.

[0095] The model generalization data of the anomaly detection includes the model generalization coefficient of the anomaly detection model; the detection effect data includes the detection efficiency coefficient and the anomaly detection accuracy coefficient.

[0096] The model generalization coefficient is an indicator used to measure the performance of anomaly detection models on unseen data. It reflects the model's ability to adapt to new data, that is, whether the rules that the model can learn from the training data can be effectively applied to unknown data. When using high-dimensional data, the model may face the problem of overfitting, especially when the amount of data is limited. The model will over-rely on the detailed information in the training set, resulting in a decrease in generalization ability. Relatively speaking, low-dimensional data can more easily capture the overall trend of the data through a simpler feature expression. Therefore, in some simple anomaly detection scenarios, low-dimensional data may show stronger generalization ability. However, too low a dimension may also lose enough details and fail to fully identify complex anomaly patterns. The generalization coefficient helps evaluate the performance of features of different dimensions in anomaly detection tasks, so as to flexibly adjust the feature extraction strategy in specific scenarios, thereby improving the detection accuracy and adaptability of the model and avoiding the problem of failing to effectively capture key anomaly patterns under specific needs.

[0097] The generalization coefficient of the analysis model is used to evaluate the anomaly detection effect when using features in different dimensions to detect anomalies. It is difficult to flexibly adjust the feature extraction strategy when performing anomaly detection in different scenarios, resulting in the inability to fully capture key anomaly patterns under specific requirements, affecting the accuracy and adaptability of detection. It has the following advantages:

[0098] Improve model adaptability: The model generalization coefficient can measure the performance of the anomaly detection model on unseen data, thereby ensuring the adaptability of the model in different scenarios. In actual applications, the operating environment and data distribution of factory equipment may vary greatly. Generalization capability evaluation can help select feature dimensions and strategies with strong adaptability.

[0099] Avoid overfitting: High-dimensional features may cause the model to perform well on training data but poorly on test data, which is called overfitting. The model generalization coefficient can effectively reflect the generalization ability of the model, thereby reducing the risk of overfitting and ensuring the stability of anomaly detection effects in practical applications.

[0100] Promote feature selection optimization: By analyzing the generalization coefficient of the model, the feature selection process can be effectively guided, helping to identify which features have better discrimination and can capture key abnormal patterns, thereby optimizing the feature extraction strategy and improving the accuracy of anomaly detection.

[0101] Enhanced detection accuracy: The evaluation of the model generalization coefficient helps to select features in different dimensions, making the detection strategy more flexible. For specific needs, selecting appropriate feature dimensions can effectively capture key abnormal patterns, reduce false positives and false negatives, and improve overall detection accuracy.

[0102] Reduce computational complexity: By evaluating the generalization coefficient, the use of high-dimensional features can be reduced, unnecessary computational overhead can be avoided, and the model can be more efficient when processing large-scale data while maintaining good detection capabilities.

[0103] Improve model stability: The generalization coefficient helps evaluate the stability of the model on different data subsets, ensuring that the anomaly detection model can maintain efficient and accurate detection capabilities even when the distribution and characteristics of the data change.

[0104] Through these advantages, the model generalization coefficient provides an effective means to solve the problem of adjusting feature extraction strategies in different scenarios, ensuring the accuracy and adaptability of anomaly detection, while improving the robustness and efficiency of the model.

[0105] The specific method for obtaining the generalization coefficient of the model is as follows:

[0106] Collect historical anomaly detection data of similar projects in the past. The historical anomaly detection data includes various types of anomaly detection features. Classify the collected anomaly detection feature records by type, assign feature weights to different types of features, and calculate the anomaly detection feature evaluation coefficient based on the type and weight of the problem record.

[0107] Obtain environmental factors that affect anomaly detection, including noise and transmission interference in the data collection environment, and calculate the impact of interference;

[0108] Obtain the type of plant equipment, the data type includes sensor data, and set a data score for the data type based on its impact on the accuracy of anomaly detection;

[0109] The model generalization coefficient is calculated by combining the interference effect, feature evaluation coefficient and data score.

[0110] The specific calculation formula of the anomaly detection feature evaluation coefficient is as follows:

[0111] ;

[0112] The specific calculation formula for interference impact is as follows:

[0113] ;

[0114] The specific calculation formula of the model generalization coefficient is as follows:

[0115] ;

[0116] In the formula, is the anomaly detection feature evaluation coefficient, is the weight of the i-th anomaly detection feature, is the number of occurrences of the i-th anomaly detection feature, is the number of times the anomaly detection feature type occurs, V is the total number of anomaly detection features, For interference effects, is the number of anomaly detection features affected, is the environmental noise, is the transmission interference, P is the plant equipment characteristics, is the model generalization coefficient.

[0117] The detection efficiency coefficient is an indicator used to evaluate the computational efficiency of anomaly detection models when performing feature extraction and data processing. High-dimensional data usually significantly increases the computational cost, especially in real-time anomaly detection tasks, which may lead to increased processing delays, thereby affecting the response speed and efficiency of the overall system. In this case, it may be necessary to use dimensionality reduction techniques (such as principal component analysis PCA) or feature selection methods to reduce the data dimension to improve computational efficiency. In contrast, low-dimensional data has a faster processing speed and consumes less computing resources, and is suitable for scenarios with high requirements for computational efficiency. However, over-simplifying data dimensions may lead to information loss, thereby affecting detection accuracy. This coefficient helps evaluate the computational efficiency of features in different dimensions when performing anomaly detection, aiming to optimize feature extraction strategies and solve the problem that improper dimensionality adjustment may affect detection accuracy and adaptability in different application scenarios.

[0118] Analyzing the detection efficiency coefficient is useful for evaluating the anomaly detection effect of features under different dimensions, so as to solve the problem that it is difficult to flexibly adjust the feature extraction strategy when performing anomaly detection in different scenarios, resulting in the inability to fully capture key anomaly patterns under specific requirements, affecting the accuracy and adaptability of detection. It has the following advantages:

[0119] Optimize computing resource utilization: By evaluating the detection efficiency coefficient, you can determine the computational efficiency of the model's features in different dimensions and help identify feature sets with low computational costs. When the data dimension is too high, the computational cost may increase significantly, especially in real-time detection scenarios, where the problem of large delays is particularly prominent. The detection efficiency coefficient can effectively reduce unnecessary computational burdens and improve the real-time response capabilities of the model.

[0120] Improve real-time performance and response speed: The detection efficiency coefficient helps ensure that the model maintains high real-time performance when processing large-scale data. By adjusting the feature dimension, selecting features with higher computational efficiency, and reducing computational latency, anomaly detection can respond more quickly to changes in the operating status of the device, especially in application scenarios that require rapid feedback of abnormal signals.

[0121] Reduce the impact of redundant features on performance: High-dimensional data often contains redundant information, which increases computational complexity and does not necessarily provide more valuable features. By evaluating the detection efficiency coefficient, it can help filter out redundant features, thereby improving computational efficiency and detection accuracy.

[0122] Improve scalability: The optimization of the detection efficiency coefficient enables the model to work efficiently in different scenarios, especially when the amount of device data is large and multiple devices need to be processed. By evaluating and selecting efficient feature combinations, the anomaly detection system can be more scalable and adapt to more complex needs.

[0123] Ensure model deployability: For features of different dimensions, the detection efficiency coefficient can help evaluate the model's computational burden and guide the adjustment of feature extraction strategies, so that the model can be efficiently deployed in different hardware and system environments. Especially in resource-constrained environments, efficient feature selection can ensure the stable operation of the model in practical applications.

[0124] Improve the balance between detection accuracy and computational efficiency: By combining the evaluation of the detection efficiency coefficient, it is possible to ensure detection accuracy while avoiding the decrease in computational efficiency caused by overly complex feature combinations. Find the best balance between computational efficiency and detection accuracy, so that anomaly detection is both accurate and efficient under specific requirements.

[0125] Improve model flexibility: The detection efficiency coefficient can provide real-time feedback for feature selection, helping to dynamically adjust feature extraction strategies according to needs in different scenarios. In this way, the model can flexibly adjust feature selection and calculation strategies according to the different needs of actual application scenarios, ensuring that anomaly detection has good adaptability in a changing industrial environment.

[0126] Through these advantages, the detection efficiency coefficient can effectively guide the feature selection process and solve the problem of being unable to flexibly adjust the feature extraction strategy in specific scenarios, thereby optimizing the computational performance and practical application effect of the anomaly detection model and improving the balance between detection efficiency and detection accuracy.

[0127] The specific method for obtaining the detection efficiency coefficient is as follows:

[0128] Obtain the error margin between the model prediction value and the actual value of several sets of feature data in the anomaly detection process;

[0129] In the same time interval, the standard deviation and mean of the error margins were calculated;

[0130] Calculate the error amplitude variation coefficient based on the signal error amplitude standard deviation and mean value;

[0131] The error amplitude variation coefficient is used to calculate the detection efficiency coefficient based on a preset detection efficiency coefficient calculation formula.

[0132] The specific calculation formula of the error amplitude variation coefficient is as follows:

[0133] ;

[0134] The specific calculation formula of the detection efficiency coefficient is as follows:

[0135] ;

[0136] In the formula, is the coefficient of variation of the error margin, is the jth error margin, is the total number of error margins during anomaly detection; is the detection efficiency coefficient.

[0137] The anomaly detection precision coefficient is an indicator used to evaluate the precision of anomaly detection models in detection tasks. High-dimensional data is usually accompanied by more noise and redundant information, which may lead to an increase in false alarms (false positives), thereby reducing the precision of the model. If the features do not have significant discrimination, the model may not perform as well in high-dimensional space as low-dimensional data. Relatively speaking, low-dimensional data helps the model to classify and make judgments more effectively by reducing redundant information, thereby improving precision. However, reducing the dimension may also lead to a decrease in recall, that is, an increase in false negatives. This precision coefficient helps to evaluate the effect of features for anomaly detection under different data dimensions, and helps solve the problem that in different scenarios, due to improper dimension selection or unreasonable feature extraction strategy, key abnormal patterns cannot be fully captured, thereby affecting the accuracy and adaptability of detection.

[0138] Analyzing the anomaly detection accuracy coefficient is useful for evaluating the anomaly detection effect when using features in different dimensions to detect anomalies. It is difficult to flexibly adjust the feature extraction strategy when performing anomaly detection in different scenarios, which leads to the inability to fully capture key anomaly patterns under specific requirements, affecting the accuracy and adaptability of detection. It has the following advantages:

[0139] Reduce false alarms and false positives: The accuracy coefficient of anomaly detection can reduce the impact of noise and redundant information and reduce the false alarm rate (false positive) by optimizing feature selection. High-dimensional data may bring redundant features, which in turn cause unnecessary false alarms. The evaluation of the accuracy coefficient can help remove these redundant features, improve the accuracy of detection, and ensure that only true anomalies are detected.

[0140] Improve the reliability of anomaly detection: By evaluating the accuracy of features in different dimensions, the anomaly detection model can better identify abnormal patterns. Especially in high-dimensional data, when the feature discrimination is low, the accuracy coefficient helps to select features with high discrimination for anomaly identification. In this way, the model can accurately identify potential problems of equipment in complex environments and enhance the reliability of anomaly detection.

[0141] Optimize the feature selection process: The accuracy coefficient can help optimize the feature selection process, especially when facing large-scale data. By evaluating the accuracy of different feature combinations, it can effectively guide the selection of more useful and efficient feature sets. This helps avoid the interference of redundant and irrelevant features, reduces model training time, and improves detection accuracy.

[0142] Improve adaptability: In different anomaly detection scenarios, the precision coefficient provides a quantitative standard to help adjust the feature extraction strategy to meet the needs of different scenarios. For example, in certain situations of equipment operation, certain types of anomalies (such as emergencies or vibrations) may be more important, and the evaluation of the precision coefficient can guide the model to optimize features, thereby improving the anomaly detection effect and adaptability in specific scenarios.

[0143] Balance precision and recall: The precision coefficient helps improve detection accuracy while avoiding sacrificing recall due to excessive precision. By evaluating the precision, we can ensure that the model has high accuracy when detecting anomalies, while avoiding excessively ignoring some smaller but still important anomalies, thus improving the overall detection performance.

[0144] Improve the ability to capture key abnormal patterns: The precision coefficient helps the model accurately identify key abnormal patterns, especially in complex or dynamic environments. By evaluating the accuracy of the feature selection process, it can ensure that the model better captures abnormal information that is critical to the safe operation of the equipment, thereby improving the equipment's fault prevention capabilities.

[0145] Enhance the interpretability of the model: Through the evaluation of the precision coefficient, the choice of feature extraction strategy becomes clearer and the decision-making process of the model becomes more interpretable. This not only helps to improve the transparency of the model in different application scenarios, but also allows relevant personnel to better understand why certain features are selected as key features, thereby providing support for decision-making.

[0146] Improve the effectiveness of the model in different scenarios: As an evaluation criterion, the precision coefficient can ensure that the features selected in different dimensions can effectively meet the anomaly detection needs in various scenarios. Whether in equipment vibration monitoring, temperature changes or other industrial parameter monitoring scenarios, the precision coefficient can guide the selection of highly adaptable and high-precision feature sets to improve the effectiveness of the model in practical applications.

[0147] Through these advantages, the anomaly detection precision coefficient can help improve the accuracy and adaptability of anomaly detection when solving the problem of not being able to flexibly adjust the feature extraction strategy under specific needs, ensuring that key abnormal patterns can be accurately captured in different scenarios and enhancing the overall detection effect of the model.

[0148] The specific method for obtaining the anomaly detection accuracy coefficient is as follows:

[0149] Obtain the waveform of predicted values ​​and actual values ​​changing over time during anomaly detection;

[0150] Under the preset frequency, the harmonic composition of the predicted value signal and the actual value signal is obtained respectively, and the harmonic component analysis is performed to obtain the basic waveform component;

[0151] The basic waveform component is converted into the harmonic component by using the inverse Fourier transform; the floating value of the harmonic is calculated according to the ratio of the basic waveform component to the harmonic component;

[0152] Data analysis is performed on the harmonic floating values ​​to obtain the anomaly detection accuracy coefficient.

[0153] In the formula, the specific calculation formula of the anomaly detection accuracy coefficient is as follows:

[0154] ;

[0155] In the formula, is the anomaly detection accuracy coefficient, is the number of harmonic components, is the actual value signal, z is the actual value signal, j is the number of harmonic components, is the inverse Fourier transform, To predict the resulting waveform, is the actual value signal waveform, is the average value of the prediction results, is the actual value signal average.

[0156] The anomaly detection evaluation model based on the bp neural network is specifically constructed as follows:

[0157] The obtained model generalization coefficient, detection efficiency coefficient and anomaly detection accuracy coefficient are used to construct an anomaly detection evaluation model based on the BP neural network to generate an anomaly detection evaluation coefficient;

[0158] The specific calculation formula of the anomaly detection evaluation coefficient is as follows:

[0159] ;

[0160] In the formula, is the anomaly detection evaluation coefficient, is the preset proportional coefficient of the model generalization coefficient, is the preset proportionality coefficient of the detection efficiency coefficient, is the preset proportional coefficient of the anomaly detection accuracy coefficient, is the model generalization coefficient, is the detection efficiency coefficient, is the anomaly detection accuracy coefficient.

[0161] This implementation performs data processing and feature extraction through multiple modules. First, the first feature acquisition module performs data conversion such as time domain, frequency domain and wavelet transform on the equipment operation data to extract the operation characteristics of the equipment; secondly, the second feature acquisition module divides the data into different windows through the sliding window method and adaptive segmentation method, and extracts the data features within the window. Then, the feature selection module optimizes the extracted features through the information gain method and principal component analysis, and selects the most representative feature set. Next, the anomaly detection evaluation module performs anomaly detection based on these feature sets, evaluates the generalization ability and detection effect of the model, and ultimately improves the accuracy and efficiency of anomaly detection. The combination of these steps helps to detect potential equipment failures in real time and accurately in complex equipment environments.

[0162] The anomaly detection application module is used to build a feature set-anomaly detection effect display model based on each set of anomaly detection feature sets to be screened and the corresponding anomaly detection evaluation model, and perform curve analysis to obtain the screened anomaly detection feature set for application to the current anomaly detection.

[0163] The feature set-anomaly detection effect display model is constructed according to each group of anomaly detection feature sets to be screened and the corresponding anomaly detection evaluation model, specifically:

[0164] Construct a vector set by combining the output of the anomaly detection evaluation model and the corresponding anomaly detection feature set to be screened;

[0165] Arrange the feature numbers of the to-be-screened anomaly detection feature sets of several vector sets from large to small as the X-axis, and the output of the corresponding anomaly detection evaluation model as the Y-axis to construct a rectangular coordinate system;

[0166] Several vector sets are marked on a rectangular coordinate system and smoothed using interpolation to construct a feature set-anomaly detection effect display model.

[0167] This embodiment can effectively evaluate the performance of different anomaly detection feature sets by constructing an anomaly detection evaluation model based on the BP neural network; by combining the model generalization coefficient, detection efficiency coefficient and anomaly detection accuracy coefficient, the model can not only improve the accuracy of anomaly detection, but also optimize the computational efficiency and generalization ability, thereby ensuring the adaptability and reliability of applications in various scenarios. By using the feature set and the anomaly detection effect display model for curve analysis, the most discriminative feature set can be systematically screened out; by analyzing the feature set, the features that can maximize the accuracy of anomaly detection and minimize the computational cost are selected, thereby improving the accuracy and efficiency of anomaly detection in practical applications; this method can flexibly adjust the feature extraction strategy during the anomaly detection process, solve the problem of not being able to fully capture key anomaly patterns in specific scenarios, and significantly improve the adaptability and accuracy of anomaly detection.

[0168] The above formulas are all dimensionless and numerical calculations. The formula is a formula for the most recent real situation obtained by collecting a large amount of data and performing software simulation. The preset parameters in the formula are set by technicians in this field according to actual conditions.

[0169] The above embodiments may be implemented in whole or in part by software, hardware, firmware or any other combination. When implemented by software, the above embodiments may be implemented in whole or in part in the form of a computer program product.

[0170] Those of ordinary skill in the art will appreciate that the modules and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of this application.

[0171] In addition, each functional module in each embodiment of the present application may be integrated into one processing module, or each module may exist physically separately, or two or more modules may be integrated into one module.

[0172] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any person skilled in the art who is familiar with the present technical field can easily think of changes or substitutions within the technical scope disclosed in the present application, which should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

[0173] Finally: The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. The plant equipment operation data analysis and anomaly detection system based on machine learning is characterized by: It includes a first feature acquisition module, a second feature acquisition module, a feature selection module, an anomaly detection evaluation module and an anomaly detection application module; A first feature acquisition module is used to acquire factory equipment operation data, perform data transformation and feature extraction on the factory equipment operation data based on a first data transformation method set, and obtain a first anomaly detection feature set; A second feature acquisition module is used to perform data segmentation of different window sizes on the factory equipment operation data based on a second data segmentation method and perform feature extraction to obtain a second anomaly detection feature set; A feature selection module is used to merge the first anomaly detection feature set and the second anomaly detection feature set to obtain a third anomaly detection feature set, and perform several dimension-up and dimension-down feature selections based on information gain method and principal component analysis to construct several groups of different anomaly detection feature sets to be screened; The anomaly detection evaluation module is used to perform anomaly detection according to several different sets of anomaly detection feature sets to be screened, obtain the model generalization data and detection effect data of anomaly detection, and build an anomaly detection evaluation model based on the BP neural network, and output the anomaly detection evaluation coefficient, which is specifically: The model generalization data of the anomaly detection includes a model generalization coefficient of the anomaly detection model, and the detection effect data includes a detection efficiency coefficient and an anomaly detection accuracy coefficient; The specific calculation formula of the anomaly detection evaluation coefficient is as follows: ; In the formula, is the anomaly detection evaluation coefficient, is the preset proportional coefficient of the model generalization coefficient, is the preset proportionality coefficient of the detection efficiency coefficient, is the preset proportional coefficient of the anomaly detection accuracy coefficient, is the model generalization coefficient, is the detection efficiency coefficient, is the anomaly detection accuracy coefficient; The anomaly detection application module is used to build a feature set-anomaly detection effect display model based on each set of anomaly detection feature sets to be screened and the corresponding anomaly detection evaluation model, and perform curve analysis to obtain the screened anomaly detection feature set for application to the current anomaly detection.

2. The machine learning-based factory equipment operation data analysis and anomaly detection system according to claim 1 is characterized in that: The first data transformation method includes time domain feature extraction, frequency domain feature extraction and wavelet transformation; The data transformation and feature extraction of the factory equipment operation data based on the first data transformation method set is specifically: By statistically analyzing the time series of plant equipment operation data, the mean, standard deviation, variance, kurtosis, and skewness are extracted as the basic distribution characteristics reflecting the equipment operation status; Using Fourier transform, the time domain data is converted into frequency domain data, and the power spectrum density, frequency peak and bandwidth are extracted as periodicity and vibration characteristics; The signal is decomposed into local features of different frequency bands through wavelet transform, and wavelet packet decomposition coefficients and wavelet energy features are extracted as burst features suitable for processing non-stationary signals. A first anomaly detection feature set is constructed according to basic distribution characteristics, periodicity and vibration characteristics, and burst characteristics.

3. The machine learning-based factory equipment operation data analysis and anomaly detection system according to claim 2 is characterized in that: The second data segmentation method includes a sliding window method and an adaptive segmentation method; The method for performing data segmentation of different window sizes on the factory equipment operation data based on the second data segmentation method and performing feature extraction is specifically: The sliding window method uses a fixed-length time window to slide over the equipment operation data at a certain step length, gradually extracting the window data features in each window; Adaptive segmentation method dynamically adjusts the window size according to the changes in the operating status of the equipment. When the equipment status is stable, a larger window is used to capture more information. When the equipment status changes dramatically, a smaller window is used to capture the changes in detail and perform data analysis to obtain the characteristics of the changed data. A second anomaly detection feature set is constructed according to the change data features and the window data features.

4. The machine learning-based factory equipment operation data analysis and anomaly detection system according to claim 3 is characterized in that: The feature selection based on information gain method and principal component analysis is performed several times of dimension increase and dimension reduction to construct several groups of different anomaly detection feature sets to be screened, specifically: Get the exception to be detected; Calculate the information gain between each feature and the anomaly to be detected, and evaluate the importance of each feature in distinguishing the device status; Select features with higher information gain; Through multiple iterations, the feature set is gradually optimized, and the third anomaly detection feature set is subjected to several dimensionality reductions to obtain several anomaly detection feature sets to be screened; Perform principal component analysis on the third anomaly detection feature set, and find the principal components in the data by calculating the covariance matrix of the features; According to the variance of the principal components, a preset number of principal components are selected to perform feature dimensionality reduction; Through the linear combination of principal components, several anomaly detection feature sets to be screened are generated; The third anomaly detection feature set is subjected to several dimensionality increase and dimensionality reduction operations to obtain several anomaly detection feature sets to be screened.

5. The machine learning-based factory equipment operation data analysis and anomaly detection system according to claim 4 is characterized in that: The specific method for obtaining the generalization coefficient of the model is as follows: Collect historical anomaly detection data of similar projects in the past. The historical anomaly detection data includes various types of anomaly detection features. Classify the collected anomaly detection feature records by type, assign feature weights to different types of features, and calculate the anomaly detection feature evaluation coefficient based on the type and weight of the problem record; Obtain environmental factors that affect anomaly detection, including noise and transmission interference in the data collection environment, and calculate the impact of interference; Obtain the type of plant equipment, the data type includes sensor data, and set a data score for the data type based on its impact on the accuracy of anomaly detection; The model generalization coefficient is calculated by combining the interference effect, feature evaluation coefficient and data score.

6. The machine learning-based factory equipment operation data analysis and anomaly detection system according to claim 5 is characterized in that: The specific method for obtaining the detection efficiency coefficient is as follows: Obtain the error margin between the model prediction value and the actual value of several sets of feature data in the anomaly detection process; In the same time interval, the standard deviation and mean of the error margins were calculated; Calculate the error amplitude variation coefficient based on the signal error amplitude standard deviation and mean value; The error amplitude variation coefficient is used to calculate the detection efficiency coefficient based on a preset detection efficiency coefficient calculation formula.

7. The machine learning-based factory equipment operation data analysis and anomaly detection system according to claim 6 is characterized in that: The specific method for obtaining the anomaly detection accuracy coefficient is as follows: Obtain the waveform of predicted values ​​and actual values ​​changing over time during anomaly detection; Under the preset frequency, the harmonic composition of the predicted value signal and the actual value signal is obtained respectively, and the harmonic component analysis is performed to obtain the basic waveform component; The fundamental waveform components are converted into harmonic components using inverse Fourier transform; Calculate the floating value of harmonics according to the ratio of the fundamental waveform component to the harmonic component; Data analysis is performed on the harmonic floating values ​​to obtain the anomaly detection accuracy coefficient.

8. The machine learning-based factory equipment operation data analysis and anomaly detection system according to claim 7, characterized in that: The feature set-anomaly detection effect display model is constructed according to each group of anomaly detection feature sets to be screened and the corresponding anomaly detection evaluation model, specifically: Construct a vector set by combining the output of the anomaly detection evaluation model and the corresponding anomaly detection feature set to be screened; Arrange the feature numbers of the to-be-screened anomaly detection feature sets of several vector sets from large to small as the X-axis, and the output of the corresponding anomaly detection evaluation model as the Y-axis to construct a rectangular coordinate system; Several vector sets are marked on a rectangular coordinate system and smoothed using interpolation to construct a feature set-anomaly detection effect display model.

9. The machine learning-based factory equipment operation data analysis and anomaly detection system according to claim 8, characterized in that: The specific calculation formula of the anomaly detection feature evaluation coefficient is as follows: ; The specific calculation formula for interference impact is as follows: ; The specific calculation formula of the model generalization coefficient is as follows: ; In the formula, is the anomaly detection feature evaluation coefficient, is the weight of the i-th anomaly detection feature, is the number of occurrences of the i-th anomaly detection feature, is the number of times the anomaly detection feature type occurs, V is the total number of anomaly detection features, For interference effects, is the number of anomaly detection features affected, is the environmental noise, is the transmission interference, P is the plant equipment characteristics, is the model generalization coefficient.

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